The Effect of Tides on the Population of PN from Interacting Binaries

TL;DR

This paper models tidal interactions in binary systems with giant stars to estimate the likelihood of planetary and stellar companions triggering planetary nebula formation, revealing a discrepancy with observed binary fractions.

Contribution

It provides new calculations of tidal capture distances during giant phases and compares these with binary period distributions to assess planetary nebula formation scenarios.

Findings

Tidal capture distances are 1-4 times the giant's maximum radius.

Only companions within 320-630 solar radii are typically captured into interaction.

Less than 2.5% of PNe should have post-common envelope binaries, lower than observed.

Abstract

We have used the tidal equations of Zahn to determine the maximum orbital distance at which companions are brought into Roche lobe contact with their giant primary, when the primary expands during the giant phases. This is a key step when determining the rates of interaction between giants and their companions. Our stellar structure calculations are presented as maximum radii reached during the red and asymptotic giant branch (RGB and AGB, respectively) stages of evolution for masses between 0.8 and 4.0 Mo (Z=0.001 - 0.04) and compared with other models to gauge the uncertainty on radii deriving from details of these calculations. We find overall tidal capture distances that are typically 1-4 times the maximum radial extent of the giant star, where companions are in the mass range from 1 Jupiter mass to a mass slightly smaller than the mass of the primary. We find that only companions at initial orbital separations between ~320 and ~630 Ro will be typically captured into a Roche lobe-filling interaction or a common envelope on the AGB. Comparing these limits with the period distribution for binaries that will make PN, we deduce that in the standard scenario where all ~1-8 Mo stars make a PN, at most 2.5 per cent of all PN should have a post-common envelope central star binary, at odds with the observational lower limit of 15-20 per cent. The observed over-abundance of post-interaction central stars of PN cannot be easily explained considering the uncertainties. We examine a range of explanations for this discrepancy.